Rectangular call a triangle, one of corners of which is equal 90 °. As well as in any other, it is possible to enter a circle in it. Such circle can be only one, its radius is defined by lengths of the parties, and the center lies in a point of intersection of bisectors of corners. It is possible to construct an inscribed circle in several ways - both with use of formulas and calculations, and without them.
It is required to you
- The drawing with a triangle, a protractor, compasses, a ruler, a pencil.
Instruction
1. Find a point which will be the center of an inscribed circle. It has to lie on crossing of bisectors of corners in triangle tops therefore at first apply a protractor to one of corners, determine its size and put the auxiliary end to the mark equal to a half of this size. Carry out a piece from top of this corner - it has to pass through an auxiliary point and end on the opposite party. In the same constructway bisector of other corner. The point of intersection of two auxiliary pieces will be the center of an inscribed circle.
2. Determine circle radius. For this purpose carry out one more auxiliary piece. It has to begin in the found point, come to an end on one of legs and to be parallel to other leg. Length of this piece will also be the radius of an inscribed circle - postpone it on compasses and draw a circle with the center in the found point. On it construction will be complete.
3. It is possible to draw an inscribed circle in a different way - with use of a formula from a course of elementary geometry. For this purpose you need to know lengths of all parties - measure them. Then calculate radius (r) - put lengths of legs (an and b), take away length of a hypotenuse (c) from result, and what turned out, divide in half: r = (a+b-c)/2. Postpone the found size on compasses and until the end of construction do not change this distance.
4. Establish compasses in top of a right angle and draw an auxiliary arch - it has to cross both legs. Actually, only points of intersection are also necessary to you therefore instead of an arch it is possible just to make tags legs. These tags specify points of contact of an inscribed circle and the parties of a triangle.
5. Establish compasses in each of points of contact and carry out two semicircles lying in a triangle. The point of their crossing will be the center of an inscribed circle - establish in it compasses and carry out the circle entered in a rectangular triangle.